| 非唯一的有理L_p逼近 |
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| 引用本文： | 潘杰,黄炳生. 非唯一的有理L_p逼近[J]. 大学数学, 1994, 0(Z1) |
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| 作者姓名： | 潘杰 黄炳生 |
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| 作者单位： | 合肥工业大学，东南大学 |
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| 摘 要： | 设f∈L_pR_m~1,p≥1。如果f在R_m~1中有无穷多个最佳逼近,则这些最佳逼近必有一致收敛的子序列,并且其极限函数也是f的最佳逼近。如果f在R_m~1中的最佳逼近都是非退化的临界点,则这些最佳逼近仅有有限个。f在R_m~1中的形如P_1(x)/(1-λx)~n的最佳逼近仅有有限个。
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| 关 键 词： | 有理逼近 非唯一性 临界点 |
Nonuniqueness of Rational L_p-Approximation |
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| Pan Jie. Nonuniqueness of Rational L_p-Approximation[J]. College Mathematics, 1994, 0(Z1) |
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| Authors: | Pan Jie |
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| Affiliation: | Pan Jie (Hefei University of Technology) Huang Bingsheng (Dongnan University) |
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| Abstract: | Let f∈L_pR_m~l If f has infinitely many best approximations in R_m~l, then they have a subsquence which is uniformly convergent and their limit is also the best approximation to f. If all the best approximations to f are nondegenerate critical points, then the number of the best approximations is finite. The number of the best L_2-approximation in R_~l such as P_t(1—λ_x)~n is finite. |
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| Keywords: | Rational approximation Nonuniqueness Critical point |
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